Wudi was the emperor who used war to bring Vietnam and Korea under Chinas control.
President Johnson's ultimate goal in Vietnam was to disengage without losing the war. This was back in history.
To prevent Communist North Vietnam from conquering the REPUBLIC of SOUTH Vietnam. To preserve the free nation of South Vietnam.
Unification was Ho Chi Minh's goal.
South Vietnam's surrender to North Vietnam is what ended the Vietnam War. The North Vietnamese had the goal of Vietnamese Unification and the surrender of South Vietnam in 1975 allowed them to achieve that objective.
They both wanted peace.
To re-unite with the Republic of South Vietnam by conquest.
To prevent South Vietnam from being taken over by communists.
Vietnam is a war which the US definitely lost because the goal of the war was to support the Republic of Vietnam (aka South Vietnam) and prevent it from falling to the Democratic Republic of Vietnam (aka North Vietnam). Despite massive effort and sacrifice on the part of the US, South Vietnam collapsed in 1975.
During the "Cold War", there were TWO Chinas: Red China & Nationalist China (Formerly called Formosa; now called Taiwan). We supplied defense material to Taiwan.
During the cold war (which ended twenty years ago) there were TWO Chinas. Which one are you questioning: Communist China or Nationalist China?
The goal of the Vietnam War was to stop the spread of communism. As such, the US felt the need to stop the influence of communist North Vietnam, which entailed supporting South Vietnam in any way possible.